What is the derivative of y=(x+7)(7sqrt(x)+2) ?

The derivative of y=(x+7)(7sqrt(x)+2) is (21x+49)/(2sqrt(x))+2

What is the first derivative of y=(x+7)(7sqrt(x)+2) ?

The first derivative of y=(x+7)(7sqrt(x)+2) is (21x+49)/(2sqrt(x))+2

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derivative of

y = (x + 7) (7 x + 2)

\frac{21 x + 49}{2 x} + 2

Solution steps

\frac{d}{d x} ((x + 7) (7 x + 2))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + 7, g = 7 x + 2

= \frac{d}{d x} (x + 7) (7 x + 2) + \frac{d}{d x} (7 x + 2) (x + 7)

\frac{d}{d x} (x + 7) = 1

\frac{d}{d x} (7 x + 2) = \frac{7}{2 x}

= 1 \cdot (7 x + 2) + \frac{7}{2 x} (x + 7)

Simplify

1 \cdot (7 x + 2) + \frac{7}{2 x} (x + 7) : \frac{21 x + 49}{2 x} + 2

= \frac{21 x + 49}{2 x} + 2

\frac{d}{d x} (x^{3} (8 - 3 x))

\frac{d}{d x} ((1 + 6 x^{2}) (x - x^{2}))

(s + 1) e^{- s π}

\frac{d y}{d x} = (x^{2})

\int (0) d x

What is the derivative of y=(x+7)(7sqrt(x)+2) ?
The derivative of y=(x+7)(7sqrt(x)+2) is (21x+49)/(2sqrt(x))+2
What is the first derivative of y=(x+7)(7sqrt(x)+2) ?
The first derivative of y=(x+7)(7sqrt(x)+2) is (21x+49)/(2sqrt(x))+2